Boundary-driven delayed-feedback control of spatiotemporal dynamics in excitable media

TL;DR

It is revealed that a novel boundary-driven mechanism suppresses meandering and chaotic spiral dynamics in a quasi-2D semidiscrete excitable model and the strength of the heterogeneities mediates the emergence of this regulation through a pinning-unpinning-like transition.

Abstract

Scroll-wave instabilities in excitable domains are central to life-threatening arrhythmias, yet practical methods to stabilize these dynamics remain limited. Here, we investigate the effects of boundary layer heterogeneities in the spatiotemporal dynamics of a quasi-2D semidiscrete excitable model. We reveal that a novel boundary-driven mechanism suppresses meandering and chaotic spiral dynamics. We show how the strength of the heterogeneities mediates the emergence of this regulation through a pinning-unpinning-like transition. We derive a reduced 2D model and find that a decrease in bulk excitability and a boundary-driven delayed-feedback underlie the stabilization. Our results may point to alternative methods to control arrhythmias.

Figures (4)

• Figure 1: Boundary layer effects. (A) Cartoon of a non-transmural ablation. (B) Schematic representation of the discrete coupling between cardiomyocytes along the transmural direction. (C) Star-like tip trajectories and the variable $u$ in the top and bottom slice for the homogeneous case at $\tau_{d}=0.382$ ms, $\mathcal{H}=14d_{z}$. (D) As in B with boundary layer heterogeneities of strength $\alpha=0.004$ and size $d_{z}$.
• Figure 2: Control of meandering instability with $l=d_{z}$. (A) $\omega$ vs $\tau_d$ in homogeneous and heterogeneous conditions. The horizontal black dashed line emphasizes $\omega_{o}(\tau_{d}^{c})$. The solid lines indicate linear fits. (B-C) Phase diagrams in $\tilde{\alpha}-\mathcal{H}/d_{z}$ space showing $\Delta\tau_{d}^{c}/\tau_{d}^{c}$ and $\omega/\omega_{o}$ at $\tau_{d}^{o}$, respectively. Here $\tilde{\alpha}=log(\alpha)+c$ with $c=10.82$logNote. The white (black) stars indicate $\max(\Delta\tau_{d}^{c}/\tau_{d}^{c})$ ($\min(\omega/\omega_{o})$) for each $\mathcal{H}$.
• Figure 3: Dynamical regimes of scroll waves. (A) $\omega$ vs $\alpha$ for different $\mathcal{H}$ in the leakage regime. (B) $\max(u_{0})$ vs $\alpha$ ($\mathcal{H}=14d_{z}$ and $l=d_{z}$). (C-D) $u_{o}$, $u_{1}$ and $u_{1}-u_{o}$ in the (C) leakage ($\alpha=4\!\times\!10^{-5}$) and (D) feedback ($\alpha=4\!\times\!10^{-3}$) regimes.
• Figure 4: $\omega$ vs $\tau_{d}$ in the different models for the case $\mathcal{H}=14d_{z}$ and $\alpha =0.005$. (A) $l\!=\!d_{z}$, (B) $l\!=\!2d_{z}$. The dashed line corresponds to the $\omega_{o}(\tau_{d}^{c})$, and the shaded area to $\Delta\tau_{d}^{c}$.